To motivate our trajectory-based approach, we want to recall that
a continuous-time system \(\dot{x}=f(x,u)\)  is flat if there exists
a one-to-one correspondence between its solutions \((x(t),u(t))\)  and
solutions \(y(t)\)  of a trivial system (sufficiently smooth but otherwise
arbitrary trajectories) with the same number of inputs (see e.g. [1]}).
